Notes On de-Sitter Mellin Barnes Amplitudes
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915664807067648 |
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| author | Choudhury, Sayantan |
| author_facet | Choudhury, Sayantan |
| contents | In this paper, we create a Mellin space method for boundary correlation functions in de Sitter (dS) and anti-de Sitter (AdS) spaces. We demonstrate that the analytic continuation between AdS${}_{d+1}$ and dS${}_{d+1}$ is encoded in a set of simple relative phases using the Mellin-Barnes representation of correlators. It helps us to determine the scalar three-point and four-point functions and their corresponding Mellin-Barnes amplitudes in dS${}_{d+1}$ space using the known results from AdS${}_{d+1}$ space. The Mellin-Barnes representation reveals the analytic structure of boundary correlation functions over all $d$ and scaling dimensions. In the present discussion, the {\it split representation} have been used as an instrumental technique in particularly the evaluation of bulk Witten diagrams and is suitable to obtain the {\it Conformal Partial Wave decomposition} of tree-level exchange in the bulk Witten diagrams. The equivalent adjustment to the cosmological three-point and four-point function of generic external scalars may be further extracted from these results, assuming the weak breakdown of the de Sitter isometries. These findings offer a step towards a more methodical comprehension of de Sitter observables utilising Mellin space techniques at the tree level and beyond. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes On de-Sitter Mellin Barnes Amplitudes Choudhury, Sayantan High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology In this paper, we create a Mellin space method for boundary correlation functions in de Sitter (dS) and anti-de Sitter (AdS) spaces. We demonstrate that the analytic continuation between AdS${}_{d+1}$ and dS${}_{d+1}$ is encoded in a set of simple relative phases using the Mellin-Barnes representation of correlators. It helps us to determine the scalar three-point and four-point functions and their corresponding Mellin-Barnes amplitudes in dS${}_{d+1}$ space using the known results from AdS${}_{d+1}$ space. The Mellin-Barnes representation reveals the analytic structure of boundary correlation functions over all $d$ and scaling dimensions. In the present discussion, the {\it split representation} have been used as an instrumental technique in particularly the evaluation of bulk Witten diagrams and is suitable to obtain the {\it Conformal Partial Wave decomposition} of tree-level exchange in the bulk Witten diagrams. The equivalent adjustment to the cosmological three-point and four-point function of generic external scalars may be further extracted from these results, assuming the weak breakdown of the de Sitter isometries. These findings offer a step towards a more methodical comprehension of de Sitter observables utilising Mellin space techniques at the tree level and beyond. |
| title | Notes On de-Sitter Mellin Barnes Amplitudes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.09175 |